定数截尾场合三参数pareto分布参数的最优置信区间  

The optimal confidence interval for the parameters of three-parameterpareto distribution in censored life test

作　　者：刘璐 李云飞[1] LIU Lu;LI Yunfei(School of Mathematic and Information, China West Normal University, Nanchong, Sichuan 637009, China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《内江师范学院学报》2022年第4期51-57,共7页Journal of Neijiang Normal University

基　　金：西华师范大学英才科研基金项目(17YC381)。

摘　　要：在定数截尾寿命试验场合下,针对三参数pareto分布的参数估计问题进行了研究.首先,在研究三参数pareto分布单总体尺度参数的最优置信区间时,使用了轮廓似然函数法和枢轴量法,然后,将这两种方法得到的置信区间进行比较,选择估计精度更高的置信区间作为尺度参数的最优置信区间.其次,研究了三参数pareto分布两总体形状参数比的最优置信区间,根据枢轴量法分别求出了形状参数比的传统置信区间和最短置信区间,通过分析发现后者估计精度更高应作为最优置信区间.最后,通过算例分析,得到这几种方法求得的置信区间作为最优置信区间的条件.The parameter estimation problem of three-parameter Pareto distribution is studied under the condition of constant censoring life test.Firstly,the optimal confidence interval of single-population parameter of three-parameter Pareto distribution is studied.The methods of profile likelihood function and the pivot quantity are used to solve the optimal confidence intervals of the scale parameter,the confidence interval with higher estimation accuracy is chosen as the optimal confidence interval of scale parameter.Secondly,the optimal confidence intervals for the ratio of two populations shape parameters of the three-parameter pareto distribution are studied.The confidence intervals are obtained by the methods of traditional probabilistic symmetry and the pivot quantity,and through analysis it finds that the optimal confidence interval is more suitable and the error is smaller than that obtained by the traditional probabilistic symmetric method,so it must be used as the optimal confidence interval.Through case analysis,the conditions that the confidence intervals thus obtained meet the standards of becoming an optimal interval are worked out.

关 键 词：定数截尾试验 三参数pareto分布 轮廓似然 最优置信区间 形状参数比 

分 类 号：O212[理学—概率论与数理统计]